(Note: This isn't an assignment problem, more a curiosity about the derivation of an equation - hopefully it is still posted in the right forum..)
I have working through the derivation for the partial molar Gibbs free energy of mixing from the Flory-Huggins expression for the Gibbs free energy of mixing, however my math skills are (very) rusty - especially when it comes to partial derivatives.
Gibbs Free Energy of Mixing (Flory-Huggins Theory):
partial molar Gibbs free energy of dilution:
ni=number of moles of i,
ϕi=volume fraction of i,
N0 is the number of lattice sites
N1 is the number of solvent molecules
N2 is the number of polymer molecules, each occupying "r" lattice sites (or "r" segments)
NA= Avogadro's constant
The Attempt at a Solution
expressing ϕ1 and ϕ2 in terms of N1 and N2 gives
Next step would be to take the partial derivative of the equation with respect to N1, I've tried many times but I cannot get anything close to the equation for the partial molar Gibbs free energy of dilution..
I broke it up, letting
taking the partial derivative
which when I plug it all back in, gives me a big mess..
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